Prediction and subtraction of multiple diffractions

ABSTRACT

Prediction and subtraction of multiple diffractions may include transforming previously acquired seismic data from a time-space domain to a transformed domain using a dictionary of compressive basis functions and separating, within the transformed previously acquired seismic data, a first portion and a second portion of the transformed previously acquired seismic data. Prediction and subtraction of multiple diffractions may also include predicting a plurality of multiple diffractions based on the separated first and second portions and adaptively subtracting the predicted multiple diffractions from the previously acquired seismic data. Prediction and subtraction of multiple diffractions may also include inverse transforming a particular seismic data set from the transformed domain to the time-space domain.

BACKGROUND

In the past few decades, the petroleum industry has invested heavily inthe development of marine seismic survey techniques that yield knowledgeof subterranean formations beneath a body of water in order to find andextract valuable mineral resources, such as oil. High-resolution seismicimages of a subterranean formation are helpful for quantitative seismicinterpretation and improved reservoir monitoring. For a typical marineseismic survey, a marine survey vessel tows one or more seismic sourcesbelow the sea surface and over a subterranean formation to be surveyedfor mineral deposits. Seismic receivers may be located on or near theseafloor, on one or more cables, also known as streamers, towed by themarine survey vessel, or on one or more cables towed by another vessel.The marine survey vessel typically contains marine seismic surveyequipment, such as navigation control, seismic source control, seismicreceiver control, and recording equipment. The seismic source controlmay cause the one or more seismic sources, which may be air guns, marinevibrators, etc., to produce acoustic impulses at selected times. Eachacoustic impulse generates a sound wave called a wavefield that travelsdown through the water and into the subterranean formation. At eachinterface between different types of rock, a portion of the wavefieldmay be refracted, and another portion may be reflected, which mayinclude some scattering, back toward the body of water to propagatetoward the sea surface. The seismic receivers thereby measure awavefield that was initiated by the actuation of the seismic source.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an elevation or xz-plane view of marine seismicsurveying in which acoustic wavefronts are emitted by a seismic sourcefor recording by seismic receivers.

FIG. 2 illustrates a diagram associated with prediction and subtractionof multiple diffractions.

FIG. 3 illustrates a diagram associated with prediction and subtractionof multiple diffractions.

FIG. 4 illustrates a diagram of a system associated with prediction andsubtraction of multiple diffractions.

FIG. 5 illustrates a diagram of a machine associated with prediction andsubtraction of multiple diffractions.

FIG. 6 illustrates a method flow diagram associated with prediction andsubtraction of multiple diffractions.

FIG. 7 illustrates a method flow diagram associated with prediction in atransformed domain and subtraction in a time-space domain.

FIG. 8 illustrates a method flow diagram associated with prediction andsubtraction in a transformed domain.

FIG. 9 illustrates a method flow diagram associated with multiplediffractions separable in a transformed domain.

DETAILED DESCRIPTION

The present disclosure is related to prediction and subtraction ofmultiple diffractions. For example, multiple diffractions may bedetected by separating transformed seismic data, predicting multiplediffractions based on the separated transformed seismic data,subtracting the multiple diffractions from the transformed seismic dataand inverse transforming the transformed seismic data. In someinstances, the transformed seismic data is transformed from a time-spacedomain to the transformed domain and inverse transformed back to thetime-space domain.

It is to be understood the present disclosure is not limited toparticular devices or methods, which may, of course, vary. It is also tobe understood that the terminology used herein is for the purpose ofdescribing particular embodiments only, and is not intended to belimiting. As used herein, the singular forms “a”, “an”, and “the”include singular and plural referents unless the content clearlydictates otherwise. Furthermore, the words “can” and “may” are usedthroughout this application in a permissive sense (i.e., having thepotential to, being able to), not in a mandatory sense (i.e., must). Theterms “comprise,” “include,” and derivations thereof, mean “comprising”or “including, but not limited to.” The term “coupled” means directly orindirectly connected.

The figures herein follow a numbering convention in which the firstdigit or digits correspond to the drawing figure number and theremaining digits identify an element or component in the drawing.Similar elements or components between different figures may beidentified by the use of similar digits. As will be appreciated,elements shown in the various embodiments herein may be added,exchanged, and/or eliminated so as to provide a plurality of additionalembodiments of the present disclosure. In addition, as will beappreciated, the proportion and the relative scale of the elementsprovided in the figures are intended to illustrate certain embodimentsof the present invention, and should not be taken in a limiting sense.

FIG. 1 illustrates an elevation or xz-plane 101 view of marine seismicsurveying in which acoustic wavefronts are emitted by a seismic sourcefor detecting and/or recording by seismic receivers for processing andanalysis in order to help characterize the structures and distributionsof features and materials underlying the surface 106 of the subterraneanformation. FIG. 1 shows a domain volume 102 comprising a subsurfacevolume 104 of sediment and rock below the surface 106 of thesubterranean formation that, in turn, underlies a fluid volume 108 ofwater having a sea surface 109 such as in an ocean, an inlet or bay, ora large freshwater lake. The domain volume 102 shown in FIG. 1represents an example experimental domain for a class of marine seismicsurveys. FIG. 1 illustrates a first sediment layer 110, an uplifted rocklayer 112, second, underlying rock layer 114, and hydrocarbon-saturatedlayer 116.

FIG. 1 shows an example of a marine survey vessel 118 equipped to carryout marine seismic surveys. In particular, the marine survey vessel 118may tow one or more cables 120 (shown as one cable for ease ofillustration) generally located near or below the sea surface 109. Thecables 120 may be long cables containing power and data-transmissionlines to which seismic receivers may be connected. In one type of marineseismic survey, each seismic receiver, such as the seismic receiverrepresented by the shaded disk 122 in FIG. 1, comprises two or moreseismic receivers including a sensor detecting particle motion,displacement velocity or acceleration, and a sensor that detectsvariations in pressure. The cables 120 and the marine survey vessel 118may include sensing electronics and data-processing facilities thatallow seismic receiver readings to be correlated with absolute positionson the sea surface and absolute three-dimensional (3D) positions withrespect to a 3D coordinate system. In FIG. 1, the seismic receiversalong the cables 120 are shown to lie below the sea surface 109, withthe seismic receiver positions correlated with overlying surfacepositions, such as a surface position 124 correlated with the positionof seismic receiver 122. The marine survey vessel 118 may also tow oneor more seismic sources 126 that produce acoustic impulses as the marinesurvey vessel 118 and cables 120 move along the sea surface 109. Anexpanding, spherical acoustic wavefront is illustrated at 128, as willbe discussed further herein with respect to FIG. 2, and is representedby circular arcs of increasing radius centered at seismic sources 126.Seismic sources 126 and/or seismic receivers 122 may also be towed byother vessels, or may be otherwise disposed in fluid volume 108. Forexample, seismic receivers may be located in ocean bottom cables ornodes fixed at or near the surface 106 of the subterranean formation,and seismic sources 126 may also be disposed in a nearly-fixed or fixedconfiguration. For the sake of efficiency, illustrations anddescriptions herein show seismic receivers located within cables, but itshould be understood that references to seismic receivers located in a“cable” or “streamer” should be read to refer equally to receiverslocated in a towed streamer, an ocean bottom seismic receiver cable,and/or an array of nodes.

FIG. 2 illustrates a diagram 221 associated with prediction andsubtraction of multiple diffractions. As noted above, FIG. 2 shows anexpanding, spherical acoustic wavefront 228, represented by circulararcs of increasing radius centered at the seismic source 226, such aswavefront 228, following an acoustic impulse emitted by the seismicsource 226. The acoustic wavefront 228 is shown in a vertical planecross section. The outward and downward expanding acoustic wavefront 228may eventually reach the surface 206 of the subterranean formation, atwhich point the outward and downward expanding acoustic wavefront 228may partially reflect 232 from the surface of the subterranean formationand may partially transmit downward into the subsurface volume, becomingwavefronts 234 within the subsurface volume. The expanding wavefront 228may also diffract and/or scatter at irregularities 230 present on thesurface 206 of the subterranean formation, thereby effectivelyinitiating the expansion of a new spherical wavefront represented bycircular arcs 236 and 238. For example, wavefront 228 hitsirregularities 230 initiating upgoing wavefront portions 236 anddowngoing wavefront portions 238. The downgoing portions 234 and 238 ofexpanding wavefronts may continue to propagate outward and downward toreach the surface of deeper subterranean formations and similarly upwardreflect, downward transmit, or diffract in all directions.

Some of the wavefronts, carrying the information utilized in the seismicimaging process, may eventually return to the sea surface and may bedetected by the seismic receivers 222 located on the cables 220 whichcan be located at or near the sea surface. In at least one embodiment,the sea surface may be surface 109 illustrated in FIG. 1. Themultiplicity of seismic wavefronts resulting from the interactionbetween the source wavefront and the subterranean interfaces betweendistinct formations may be referred to as a seismic wavefield.Individual wavefronts constituting the seismic wavefield may also bereferred to as seismic events. The signals recorded by the seismicreceivers at a plurality of spatial locations and sampled at a pluralityof temporal delays with respect to the ignition of the seismic sourcemay be referred to as seismic data.

Seismic events are classified based on their propagation history insidethe subsurface. Primaries are seismic events whose propagation historyincludes exactly one upward reflection or a diffraction (scattering)episode in the subsurface. Multiples are seismic events characterized byat least two upward reflections or diffractions in the subsurface,separated by at least one downward reflection at the sea surface.Multiple reflections (or reflected multiples) consist of eventscharacterized by at least one subsurface upward reflection, followed bya downward reflection at the sea surface, followed by at least anotherupward reflection in the subsurface. Multiple diffractions (ordiffracted multiples) may consist of events characterized by at leastone subsurface diffraction, followed by a downward reflection at the seasurface, followed by at least another diffraction in the subsurface.Multiple diffractions also may include events characterized, forexample, by an upward subsurface reflection, followed by a downwardreflection at the sea surface, followed by a subsurface diffraction.Similarly, multiple diffractions may include events characterized by asubsurface diffraction, followed by a downward reflection at the seasurface, followed by an upward subsurface reflection.

Multiples may be considered noise, and it may be desirable to removethese multiples prior to seismic imaging. However, the removal ofmultiple diffractions may be challenging due to their steeply dipping,heavily aliased tails, for example. For instance, multiple diffractionsmay become indistinguishable from one another and/or may displaydifferently in different domains. In contrast, at least one embodimentof the present disclosure provides improved multiple diffractiondetection.

In at least one embodiment, a compressive domain transform may beutilized to map seismic data from the time-space domain to a transformeddomain where individual points, or a small group of points, mayrepresent the recorded signals associated with a specific event, forexample a multiple diffraction, or other events in the time-spacedomain. As used herein, the time-space domain comprises an analysis ofmathematical functions, physical signals, and/or environmental data withrespect to time and/or space. The transformed domain, as used herein,comprises a mathematical procedure done in data that converts it fromone domain, such as a time or time-space domain, to another domain suchas a frequency domain. In at least one embodiment, the compressivetransform utilized is an Asymptote and Apex Shifted Hyperbolic RadonTransform (AASHRT). In another embodiment, the compressive transformutilized is based on a dictionary of Green's functions for a homogeneousmedium. Dictionaries, as used herein, include a set of signals calledatoms describing elementary features and can be locally trained tocapture a morphology associated with seismic data.

As used herein, seismic data comprises data associated with a wavefield.For instance, seismic data may include data associated with time, space,and amplitudes of wavefields. Sampled seismic data comprises sampledand/or recorded seismic data. Seismic data may be sampled from a seismicreceiver located on a cable, an ocean bottom cable, or a node, amongothers. Previously acquired seismic data includes seismic data that hasalready be sampled and/or collected by another means.

In the compressed domain, the events corresponding to specificevent-types in the seismic wavefield may become distinguishable. Forexample, it may become possible to distinguish a predominantlyreflective portion of the transformed wavefield from a predominantlydiffractive portion of the transformed wavefield. As used herein,predominantly refers to having the most importance or influence. Forinstance, a predominantly reflective portion may have properties thatare not reflective, but the reflective property has a greater importanceor influence than the other properties. The predominantly diffractiveportion may have properties that are not diffractive, but thediffractive property has a greater importance or influence than theother properties. The two portions may be complementary, so that theirsum may amount to the transformed wavefield. The separation may be basedon an equivalent source delay parameter of a Green's function baseddictionary or on an asymptote shift parameter associated with the AASHRTdictionary. The asymptote shift parameter can include a quantity whosevalue is selected for particular circumstances and in relation to anasymptote shift. The equivalent source delay parameter can include aquantity whose value is selected for particular circumstances and inrelation to a source delay.

The inverse transform of the predominantly diffractive portion of thetransformed wavefield may be utilized to obtain an estimate ofdiffractions in the original seismic data. That estimate may be used ina prediction process, in order to obtain a prediction of the multiplediffractions in the seismic data. As used herein, an inverse transformperforms the reverse or opposite of a forward transform. For example, itmay reconstruct seismic data which, if forward transformed, would giveback the transformed seismic data which is the input to the inversetransform.

In at least one embodiment, the prediction process is a surface-relatedmultiple elimination (SRME) process. SRME is a demultiple tool aimed atremoving multiple energy derived from an air/water interface. DuringSRME, seismic data is used to predict and iteratively subtract amultiple series. It may be, in one embodiment, that the inversetransform allows the output estimate of diffractions in the originalseismic data to be interpolated at a denser spacing than the originalinput seismic data, such that the prediction process may work optimallyby avoiding what may be heavily aliased events otherwise. Subsequently,that prediction resulting from the prediction process may be adaptivelysubtracted from the original seismic data to remove multiplediffractions. As used herein, adaptively subtracting includes making thesubtraction process suitable to conditions of the prediction and theoriginal seismic data. Adaptive subtraction is an element used indata-driven multiple-suppression methods to minimize misalignments andamplitude differences between predicted and actual multiples, and mayreduce multiple contaminations in a data set after subtraction.

In at least one embodiment, the prediction process may be performed inthe transformed domain. The inverse transform may be applied to themultiple diffraction prediction, resulting from the prediction processin the transformed domain. The multiple diffraction prediction may thenbe adaptively subtracted from the initial seismic wavefield in thetime-space domain.

In another embodiment, both the prediction process and the adaptivesubtraction may be performed in the transformed domain. The inversetransform of seismic data without multiple diffractions to thetime-space domain may be utilized.

In the transformed domain, multiple diffractions may becomedistinguishable from primaries and other types of multiples. In at leastone embodiment, the portions of the transformed domain identified asmultiple diffractions may be muted, so that an inverse transform appliedto the remaining portion of the transformed seismic data may generateseismic data free of multiple diffractions. As used herein, mutedseismic data is seismic data with multiple diffractions removed. Inanother embodiment, the inverse transform may be applied only to theportions of the transformed seismic data identified as multiplediffractions. The resulting estimate of multiple diffractions in thetime-space domain may then be subtracted or adaptively subtracted fromthe initial seismic data.

Compressive transforms may rely on a dictionary that, as used herein,consists of a plurality of basis functions or frames. Measurements ofthe seismic wavefield may be described as a superposition of those basisfunctions, each scaled by an appropriate real or complex-valued spectralcoefficient. The collection of all spectral coefficients pertaining toall employed basis functions constitutes the transformed domain. As usedherein, a dictionary of basis functions includes a collection of Green'sfunctions for the homogeneous medium, and a collection of apex andasymptote shifted hyperbolic functions (AASHRT dictionary). The AASHRTdictionary may perform similarly, but not exactly as the Green'sfunction dictionary.

Within the Green's function dictionary, each basis function may bechosen as the wavefield which would be recorded at the seismic receiverlocations r={x, y, z} if an instantaneous point source were fired attime t′ at a generic location r′={x′, y′, z′} of a fictitioushomogeneous reference medium characterized by a constantwave-propagation velocity c. Basis functions G may be written as:

${G\left( {t,r,t^{\prime},r^{\prime}} \right)} = {{\frac{1}{{r - r^{\prime}}}{H\left( {t,r,t^{\prime},r^{\prime}} \right)}} = {\frac{1}{{r - r^{\prime}}}{{\delta\left( {t - \left( {t^{\prime} + \frac{{r - r^{\prime}}}{c}} \right)} \right)}.}}}$

The hyperbolic term

${H\left( {t,r,t^{\prime},r^{\prime}} \right)} = {\delta\left( {t - \left( {t^{\prime} + \frac{{r - r^{\prime}}}{c}} \right)} \right)}$defines the basis functions used within the AASHRT dictionary. Using adifferent but equivalent parameterization, the basis functions in theAASHRT dictionary may be defined as:

${H\left( {t,x,y,z,t^{\prime},x^{\prime},y^{\prime},\tau} \right)} = {\delta\left( {t - \left( {t^{\prime} + \sqrt{\tau^{2} + \frac{\left( {x - x^{\prime}} \right)^{2} + \left( {y - y^{\prime}} \right)^{2}}{c^{2}}}} \right)} \right)}$where the parameter

$\tau = \frac{z - z^{\prime}}{c}$represents the temporal location of the hyperbola's apex. Similarly,parameters x′ and y′represent the spatial location of the hyperbola'sapex. The parameter t′, previously introduced as a firing delayparameter for the Green's function dictionary, may be seen as a temporalasymptote shift in the context of the AASHRT dictionary. The firingdelay parameter can include a quantity whose value is selected forparticular circumstances and in relation to delay in an actuation of aseismic source (also referred to as firing).

For the case of 3D wave propagation, each basis function in the Green'sfunction dictionary and in the AASHRT dictionary may be unambiguouslyidentified by a unique combination of five spectral parameters: t′, x′,y′, z′, and c. In the case of two-dimensional (2D) propagation, basisfunctions may be identified by a unique combination of four spectralparameters: t′, x′, z′, and c. Using the second parameterization, 3Dbasis functions may be similarly identified by a unique combination offive parameters: t′, x′, y′, τ, and c. Two-dimensional basis functionsare defined by unique combinations of four parameters: t′, x′, τ, and c.

FIG. 3 illustrates a diagram associated with prediction and subtractionof multiple diffractions along a time axis 360 and a space axis 350. Forexample, FIG. 3 illustrates a diagram associated with representingseismic data in a compressed domain, based on the above-describeddictionaries. FIG. 3 is an example 2D diagram, so the apex location isdetermined by one horizontal coordinate, x′. For example, each hyperbola340 may be parameterized in terms of apex time τ 364, asymptote shift t′362 (associated with the intersection of the hyperbola's asymptotes),the location of the hyperbola's apex x′ 352, the shape or dip 344 of theasymptotes 342 for large offsets (in meters) and times (in seconds).Asymptote dip may be associated with the ratio 344 between theinstantaneous variation of time dt and space dx along the tails of ahyperbola. This ratio may be described as the inverse of a velocity (inmeters/seconds) as shown in FIG. 3. In an example 3D representation, theapex location may be described by two horizontal coordinates, x′ and y′.

Using either of the two dictionaries L, seismic data in the time-spacedomain d(t, x, y) may be represented as a superposition of hyperbolicevents and mapped to the transformed domain m(e, x′, y′, z′, c) or m(e,x′, y′, τ, c)

${d\left( {t,x,y} \right)} = {{\sum\limits_{t^{\prime},x^{\prime},y^{\prime},z^{\prime},c}\;{{Lm}\left( {t^{\prime},x^{\prime},y^{\prime},\tau,c} \right)}} = {\sum\limits_{x^{\prime},y^{\prime},z^{\prime},c}{{m\left( {\sqrt{\tau^{2} + \frac{\left( {x - x^{\prime}} \right)^{2} + \left( {y - y^{\prime}} \right)^{2}}{c^{2}}},x^{\prime},y^{\prime},t^{\prime},c} \right)}.}}}$

Seismic data in the compressed domain {tilde over (m)}, using theadjoint L* of either of the two dictionaries, may be estimated through asummation performed on the seismic data in the time-space domain alonghyperbolic trajectories

${\overset{\sim}{m}\left( {t^{\prime},x^{\prime},y^{\prime},\tau,v} \right)} = {{\sum\limits_{t,x,y}\;{L*{d\left( {t,x,y} \right)}}} = {\sum\limits_{x,y}\;{{d\left( {{t^{\prime} + \sqrt{\tau^{2} + \frac{\left( {x - x^{\prime}} \right)^{2} + \left( {y - y^{\prime}} \right)^{2}}{c^{2}}}},x,y} \right)}.}}}$

FIG. 4 illustrates a diagram of a system 470 associated with predictionand subtraction of multiple diffractions. The system 470 may include adata source 472, a subsystem 474, and/or a plurality of engines such asanalysis engine 481, separation engine 482, prediction engine 480,subtraction engine 483, and/or synthesis engine 476, and may be incommunication with the data source 472 (or data store) via acommunication link. The subsystem 474 may include additional or fewerengines than listed to perform the various functions described herein.The system 474 may represent program instructions and/or hardware of amachine such as machine 784. As used herein, an “engine” may includeprogram instructions and/or hardware, but at least includes hardware.Hardware is a physical component of a machine that enables it to performa function. Examples of hardware may include a processing resource, amemory resource, a logic gate, etc.

The plurality of engines 481, 482, 480, 483, 476 may include acombination of hardware and program instructions that is configured toperform a plurality of functions described herein. The programinstructions, such as software, firmware, etc., may be stored in amemory resource such as a machine-readable medium, as well as hard-wiredprogram such as logic. Hard-wired program instructions may be consideredas both program instructions and hardware. An analysis engine 481 mayinclude a combination of hardware and program instructions configured totransform previously acquired seismic data from a time-space domain to atransformed domain using a dictionary of compressive basis functions.Transforming the previously acquired seismic data includes changing theform of the previously acquired seismic data from one domain to another.In at least one embodiment, the dictionary of compressive basisfunctions comprises a transform dictionary composed of AASHRT functions.In another embodiment, the dictionary of compressive basis functionscomprises a transform dictionary composed of Green's functions forhomogeneous media. A transform dictionary includes functions associatedwith transforming the previously acquired seismic data.

A separation engine 482 may include a combination of hardware andprogram instructions configured to separate, within the transformedpreviously acquired seismic data, a first portion and a second portionof the previously acquired seismic data. Separation can includesplitting the previously acquired data into a plurality of portionsbased on particular characteristics of the previously acquired seismicdata. In at least one embodiment, the first portion is associated withmultiple diffractions, and the second portion is the remainder of thetransformed seismic data. In such an embodiment, synthesis engine 476(discussed further below) may be configured to inverse transform aremainder of transformed previously acquired seismic data to thetime-space domain.

In at least one embodiment, the first portion is a reflective portion,and the second portion is a diffractive portion. The first portion maybe a predominantly reflective portion and the second portion may be apredominantly diffractive portion. Separation engine 482 may alsoseparate the reflective portion and the diffractive portion based on afiring delay parameter or an asymptote shift parameter associated withthe dictionary of basis functions. In at least one embodiment, theseparation engine may be configured to separate, within the transformeddomain, a portion related to multiple diffractions.

A prediction engine 480 may include a combination of hardware andprogram instructions configured to predict, within the transformeddomain and/or the time-space domain, a plurality of multiplediffractions based on the separated first and second portions, and/orbased on a combination of one of the separated portions and the entiretyof the transformed seismic data. In at least one embodiment, theprediction engine 480 is configured to predict the plurality of multiplediffractions based on the separated diffractive portion. In anotherembodiment, the prediction engine 480 may be configured to predict amultiplicity of multiple diffractions based on a combination of thetransformed seismic data and the separated diffracted portion of thetransformed seismic data. In at least one embodiment, the predictionengine may be configured to predict a multiplicity of multiplediffractions in the time-space domain. The prediction engine 480 may beconfigured to predict the plurality of multiple diffractions based onthe separated diffractive portion after an inverse transform. In anotherembodiment, the prediction engine may be configured to predict theplurality of multiple diffractions based on a combination of thepreviously acquired seismic data and the inverse transformed diffractedportion.

A subtraction engine 483 may include a combination of hardware andprogram instructions configured to adaptively subtract the plurality ofmultiple diffractions from the previously acquired seismic data. In atleast one embodiment, the subtraction engine operates on seismic datawithin the transformed domain. In other embodiments, the subtractionengine operates on seismic data within the time-space domain.

A synthesis engine 476 may include a combination of hardware and programinstructions configured to inverse transform a particular seismic dataset from the transformed domain to the time-space domain. A particularseismic data set can include a portion of the previously acquiredseismic data set. For instance, the particular seismic data set caninclude a predicted plurality of multiple diffractions and/or aseparated diffractive portion. In at least one embodiment, thetransformed seismic data may include a predominantly reflective portionor predominantly diffractive portion of the transformed seismic data.The synthesis engine may be configured to output seismic data in thetime-space domain at denser locations than the seismic data input to theanalysis engine. In another embodiment, the transformed seismic data mayinclude the predicted multiple diffractions. In yet another embodiment,the transformed seismic data may include the seismic data aftersuppression of multiple diffractions.

In at least one embodiment, the prediction engine is configured topredict, within the transformed domain, the plurality of multiplediffractions based on the separated predominantly diffractive portion,the synthesis engine is configured to inverse transform the predictedplurality of multiple diffractions, and the subtraction engine isconfigured to subtract, in the time-space domain, the inversetransformed multiple diffractions from the previously acquired seismicdata.

In another embodiment, the synthesis engine is configured to inversetransform the separated predominantly diffractive portion, theprediction engine is configured to predict, within the time-spacedomain, the plurality of multiple diffractions based on the separatedinverse-transformed diffractive portion, and the adaptive subtractionengine is configured to subtract, in the time-space domain, the inversetransformed predicted multiple diffractions from previously acquiredseismic data.

In at least one embodiment, the prediction engine is configured topredict, within the transformed domain, the plurality of multiplediffractions based on the separated predominantly diffractive portion,the adaptive subtraction engine is configured to subtract, in thetransformed domain, the predicted multiple diffractions from thetransformed previously acquired seismic data, and the synthesis engineis configured to inverse transform the result to the time-space domain.

FIG. 5 illustrates a diagram of a machine 584 associated with predictionand subtraction of multiple diffractions. The machine 584 may utilizesoftware, hardware, firmware, and/or logic to perform a plurality offunctions. The machine 584 may be a combination of hardware and programinstructions configured to perform a plurality of functions. Thehardware, for example, may include a plurality of processing resources586 and a plurality of memory resources 588, such as a machine-readablemedium or other memory resources.

The memory resources 588 may be internal and/or external to the machine584, for example, the machine 584 may include internal memory resourcesand have access to external memory resources. The program instructions,such as machine-readable instructions, may include instructions storedon the machine-readable medium to implement a particular function, forexample, an action such as prediction and subtraction of multiplediffractions. The set of machine-readable instructions may be executableby one or more of the processing resources 586. The memory resources 588may be coupled to the machine in a wired and/or wireless manner. Forexample, the memory resources 588 may be an internal memory, a portablememory, a portable disk, and/or a memory associated with anotherresource, for example, enabling machine-readable instructions to betransferred and/or executed across a network such as the Internet. Asused herein, a “module” may include program instructions and/orhardware, but at least includes program instructions.

Memory resources may be non-transitory and may include volatile and/ornon-volatile memory. Volatile memory may include memory that dependsupon power to store information, such as various types of dynamic randomaccess memory among others. Non-volatile memory may include memory thatdoes not depend upon power to store information. Examples ofnon-volatile memory may include solid state reference media such asflash memory, electrically erasable programmable read-only memory, phasechange random access memory, magnetic memory, optical memory, and/or asolid state drive, etc., as well as other types of non-transitorymachine-readable media.

The processing resources 586 may be coupled to the memory resources viaa communication path 590. The communication path 590 may be local orremote to the machine. Examples of a local communication path mayinclude an electronic bus internal to a machine, where the memoryresources 588 are in communication with the processing resources 586 viathe electronic bus. Examples of such electronic buses may includeIndustry Standard Architecture, Peripheral Component Interconnect,Advanced Technology Attachment, Small Computer System Interface,Universal Serial Bus, among other types of electronic buses and variantsthereof. The communication path 590 may be such that the memoryresources are remote from the processing resources, such as in a networkconnection between the memory resources and the processing resources.That is, the communication path 590 may be a network connection.Examples of such a network connection may include a local area network,wide area network, personal area network, and the Internet, amongothers.

The machine-readable instructions stored in the memory resources 588 maybe segmented into a plurality of modules 592, 587, 585 that whenexecuted by the processing resources may perform a plurality offunctions. As used herein, a module includes a set of instructionsincluded to perform a particular task or action. The plurality ofmodules may be sub-modules of other modules. Each of the plurality ofmodules 592, 587, 585, 593 may include program instructions and/or acombination of hardware and program instructions that, when executed bya processing resource, may function as a corresponding engine.

An analysis module 592 may include instructions executable to transformpreviously acquired seismic data from a time-space domain to atransformed domain using a dictionary of basis functions. In at leastone embodiment, the dictionary of basis functions comprises a transformdictionary composed of AASHRT functions. In another embodiment, thedictionary of basis functions comprises a transform dictionary composedof Green's functions for homogeneous media.

A separation module 587 may include instructions executable to separate,within the previously acquired seismic data, a reflective portion and adiffractive portion and predict a plurality of multiple diffractionsbased on the separated diffractive portion. Separation module 587 mayalso include instructions executable to separate the reflective portionand the diffractive portion based on an asymptote shift parameterassociated with the dictionary of basis functions.

A synthesis module 585 may include instructions executable to inversetransform a particular seismic data set from the transformed domain tothe time-space domain. In at least one embodiment, a subtraction module593 may include instructions executable to adaptively subtract theinverse transformed particular seismic data set from the previouslyacquired seismic data.

FIGS. 6-9 illustrate method flow diagrams associated with prediction andsubtraction of multiple diffractions. Elements illustrated in FIG. 6-9may be performed in an order other than that presented in the Figuresfrom top to bottom. FIG. 6 illustrates a method flow diagram 694associated with prediction and subtraction of multiple diffractions. At695, previously acquired seismic data may be transformed from atime-space domain to a transformed domain using a dictionary of basisfunctions. The dictionary may comprise a dictionary of AASHRT basisfunctions and a Green's function dictionary. At 696, a reflectiveportion and a diffractive portion may be separated within the previouslyacquired seismic data. The reflective portion may be predominantlyreflective and the diffractive portion may be predominantly diffractive.In at least one embodiment, the predominantly reflective portion and thepredominantly diffractive portion may be separated based on an asymptoteshift parameter associated with the dictionary of AASHRT basis functionsand a firing delay parameter associated with the Green's functiondictionary.

At 668, a plurality of multiple diffractions may be predicted based onthe separated diffractive portion. The prediction may occur within thetransformed domain and/or within the time-space domain. In at least oneembodiment, predicting the plurality of multiple diffractions within thetime-space domain comprises predicting the plurality of multiplediffractions using a surface-related multiple elimination predictionbased on a combination of the separated diffractive portion and thepreviously acquired seismic data.

The method may include, at 698, inverse transforming a first particularseismic data set from the transformed domain to the time-space domain.In at least one embodiment, inverse transforming the first particularseismic data set comprises inverse transforming the predicted pluralityof multiple diffractions. In another embodiment, inverse transformingthe first particular seismic data set comprises inverse transforming theseparated diffractive portion. The separated diffractive portion may beinverse transformed such that the separated diffractive portion issynthesized at denser locations than the previously acquired seismicdata. For example, the locations of the synthesis may be more compactthan during acquisition of the seismic data.

At 699, a second particular seismic data set may be adaptivelysubtracted from previously acquired seismic data. The adaptivesubtraction may occur within the transformed domain and/or within thetime-space domain. For example, adaptively subtracting may includeadaptively subtracting, within the transformed domain and/or thetime-space domain the predicted multiple diffractions from thepreviously acquired seismic data. In at least one embodiment, the secondparticular seismic data set that is adaptively subtracted is a result ofthe inverse transforming. In another embodiment, the second particularseismic data set that is adaptively subtracted is a result of thepredicting. In at least one embodiment, the method 694 can includeconducting a marine survey to acquire seismic data and/or acquiring theseismic data from a third party.

FIG. 7 illustrates a method flow diagram 730 associated with predictionin a transformed domain and subtraction in a time-space domain. At 731,previously acquired seismic data is transformed from a time-space domainto a transformed domain using a dictionary of basis functions. Thedictionary may comprise a dictionary of AASHRT basis functions and aGreen's function dictionary.

At 732, a predominantly reflective portion and a predominantlydiffractive portion are separated from within the transformed seismicdata. In at least one embodiment, the predominantly reflective portionand the predominantly diffractive portion may be separated based on anasymptote shift parameter associated with the dictionary of AASHRT basisfunctions and a firing delay parameter associated with the Green'sfunction dictionary.

At 733, a plurality of multiple diffractions is predicted within thetransformed domain based on the separated reflective and diffractiveportions. The predicted multiple diffractions may be inverse transformedto the time-space domain at 734, and the multiple diffractions may beadaptively subtracted within the time-space domain from the transformedseismic data at 735. In at least one embodiment, the method can includeconducting a marine survey to acquire seismic data and/or acquiring theseismic data from a third party.

FIG. 8 illustrates a method flow diagram 836 associated with predictionand subtraction in a transformed domain. At 837, previously acquiredseismic data from a time-space domain may be transformed to atransformed domain using a dictionary of basis functions. At 838, apredominantly reflective portion and a predominantly diffractive portionmay be separated within the transformed seismic data. A plurality ofmultiple diffractions may be predicted within the transformed domain at839, for example based on the separated predominantly reflective andpredominantly diffractive portions. At 841, the multiple diffractionsmay be adaptively subtracted, within the transformed domain, from thetransformed seismic data. The seismic data may be inverse transformed tothe time-space domain at 843. In at least one embodiment, the method caninclude conducting a marine survey to acquire seismic data and/oracquiring the seismic data from a third party.

FIG. 9 illustrates a method flow diagram 970 associated with multiplediffractions separable in a transformed domain. At 971, previouslyacquired seismic data may be transformed from a time-space domain to atransformed domain using a dictionary of basis functions. At 972, aportion of the transformed previously acquired seismic data associatedwith the plurality of multiple diffractions may be muted. The muting maybe based on an equivalent source delay parameter and an asymptote shiftparameter associated with the dictionary of basis functions in at leaston embodiment.

The remaining unmuted portion of the transformed seismic data may beinverse transformed to the time-space domain at 973. For example, theremainder of the transformed seismic data may be the remainder of thetransformed seismic data after the muting, such that the seismic datahas multiple diffractions removed. In another embodiment, the multiplediffractions may be brought back and later subtracted from the inputseismic data. Inverse transforming the remaining unmuted portion mayinclude inverse transforming a primary associated with the transformedpreviously acquired seismic data in at least one embodiment. A primary,also called a primary reflection, can include a seismic wave that hasbeen reflected only once before being detected by a seismic receiver, incontrast to a multiple reflection. In at least one embodiment, themethod can include conducting a marine survey to acquire seismic dataand/or acquiring the seismic data from a third party.

In accordance with a plurality of embodiments of the present disclosure,a geophysical data product may be produced. For instance, a geophysicaldata product may be generated from at least one of the previouslyacquired seismic data and the plurality of multiple diffractions.Geophysical data, such as data sampled by seismic receivers, depthsensors, location sensors, etc., may be obtained and stored on anon-transitory, tangible machine-readable medium. The geophysical dataproduct may be recorded on a non-transitory machine-readable mediumsuitable for importing onshore. The geophysical data product may beproduced by processing the geophysical data offshore or onshore eitherwithin the United States or in another country. If the geophysical dataproduct is produced offshore or in another country, it may be importedonshore to a facility in the United States. In some instances, onceonshore in the United States, geophysical analysis/processing may beperformed on the geophysical data product. In some instances,geophysical analysis/processing may be performed on the geophysical dataproduct offshore. For example, recorded seismic data may be treatedaccording to the present disclosure as the recorded seismic data issampled and/or measured offshore to facilitate other processing of theseismic data either offshore or onshore.

Although specific embodiments have been described above, theseembodiments are not intended to limit the scope of the presentdisclosure, even where only a single embodiment is described withrespect to a particular feature. Examples of features provided in thedisclosure are intended to be illustrative rather than restrictiveunless stated otherwise. The above description is intended to cover suchalternatives, modifications, and equivalents as would be apparent to aperson skilled in the art having the benefit of this disclosure.

The scope of the present disclosure includes any feature or combinationof features disclosed herein (either explicitly or implicitly), or anygeneralization thereof, whether or not it mitigates any or all of theproblems addressed herein. Various advantages of the present disclosurehave been described herein, but embodiments may provide some, all, ornone of such advantages, or may provide other advantages.

What is claimed is:
 1. A system, comprising: an analysis hardware engineconfigured to transform previously acquired seismic data acquired at aplurality of locations from a time-space domain to a transformed domainusing a dictionary of asymptote- and apex-shifted hyperbolic radontransform (AASHRT) basis functions and a dictionary of Green'sfunctions; a separation hardware engine configured to separate, withinthe transformed previously acquired seismic data, a first portion and asecond portion of the transformed previously acquired seismic data basedon an asymptote shift parameter associated with the dictionary of AASHRTbasis functions and a firing delay parameter associated with thedictionary of Green's functions; a prediction hardware engine configuredto predict, a plurality of multiple diffractions based on the separatedfirst and second portions; a subtraction hardware engine configured toadaptively subtract the predicted multiple diffractions from thepreviously acquired seismic data; and a synthesis hardware engineconfigured to inverse transform a particular seismic data set from thetransformed domain to the time-space domain such that the separateddiffractive portion is synthesized at denser locations than thepreviously acquired seismic data, wherein the denser locations are morecompact with respect to one another as compared to the pluralitylocations during acquisition of the previously acquired seismic data. 2.The system of claim 1, wherein the first portion is a predominantlyreflective portion and the second portion is a predominantly diffractiveportion.
 3. The system of claim 2, wherein the prediction engine isconfigured to predict, within the transformed domain, the plurality ofmultiple diffractions based on the separated predominantly diffractiveportion, the synthesis engine is configured to inverse transform theplurality of multiple diffractions, and the subtraction engine isconfigured to subtract, in the time-space domain, the inversetransformed multiple diffractions from the previously acquired seismicdata.
 4. The system of claim 2, wherein the synthesis engine isconfigured to inverse transform the separated predominantly diffractiveportion, the prediction engine is configured to predict, within thetime-space domain, the plurality of multiple diffractions based on theseparated inverse-transformed diffractive portion, and the adaptivesubtraction engine is configured to subtract, in the time-space domain,the inverse transformed predicted multiple diffractions from previouslyacquired seismic data.
 5. The system of claim 2, wherein the predictionengine is configured to predict, within the transformed domain, theplurality of multiple diffractions based on the separated predominantlydiffractive portion, the adaptive subtraction engine is configured tosubtract, in the transformed domain, the predicted multiple diffractionsfrom the transformed previously acquired seismic data, and the synthesisengine is configured to inverse transform the result to the time-spacedomain.
 6. The system of claim 1, wherein the first portion isassociated with multiple diffractions and the second portion is aremainder of the transformed previously acquired seismic data, and thesynthesis engine is configured to inverse transform the remainder of thetransformed previously acquired seismic data to the time-space domain.7. A method, comprising: transforming previously acquired seismic dataacquired at a plurality of locations from a time-space domain to atransformed domain using a dictionary of asymptote- and apex-shiftedhyperbolic radon transform (AASHRT) basis functions and a dictionary ofGreen's functions; separating, within the transformed previouslyacquired seismic data, a reflective portion and a diffractive portionbased on an asymptote shift parameter associated with the dictionary ofAASHRT basis functions and a firing delay parameter associated with thedictionary of Green's functions; predicting a plurality of multiplediffractions based on the separated diffractive portion; inversetransforming a first particular seismic data set from the transformeddomain to the time-space domain such that the separated diffractiveportion is synthesized at denser locations than the previously acquiredseismic data, wherein the denser locations are more compact with respectto one another as compared to the plurality locations during acquisitionof the previously acquired seismic data; adaptively subtracting a secondparticular seismic data set from the previously acquired seismic data;and recording a result of the adaptive subtraction on a non-transitorymachine-readable medium.
 8. The method of claim 7, wherein predictingthe plurality of multiple diffractions comprises predicting, within thetransformed domain, the plurality of multiple diffractions.
 9. Themethod of claim 7, wherein predicting the plurality of multiplediffractions comprises predicting, within the time-space domain, theplurality of multiple diffractions.
 10. The method of claim 9, whereinpredicting the plurality of multiple diffractions within the time-spacedomain comprises predicting the plurality of multiple diffractions usinga surface-related multiple elimination prediction based on a combinationof the separated diffractive portion and the previously acquired seismicdata.
 11. The method of claim 7, wherein inverse transforming the firstparticular seismic data set comprises inverse transforming the predictedplurality of multiple diffractions.
 12. The method of claim 7, whereininverse transforming the first particular seismic data set comprisesinverse transforming the separated diffractive portion.
 13. The methodof claim 12, wherein inverse transforming the separated diffractiveportion such that the separated diffractive portion is synthesized atdenser locations than the previously acquired seismic data comprisessynthesizing the separated diffractive portion at a more compactlocation as compared to a synthesis location of the previously acquiredseismic data.
 14. The method of claim 7, wherein adaptively subtractingthe second particular seismic data set comprises adaptively subtracting,within the transformed domain, the plurality of predicted multiplediffractions from the previously acquired seismic data.
 15. The methodof claim 7, wherein adaptively subtracting the second particular seismicdata set comprises adaptively subtracting, within the time-space domain,the inverse transformed plurality of predicted multiple diffractionsfrom the previously acquired seismic data.